Reflected Brownian Motions in the KPZ Universality Class

This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, be...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Weiss, Thomas (Συγγραφέας), Ferrari, Patrik (Συγγραφέας), Spohn, Herbert (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2017.
Σειρά:SpringerBriefs in Mathematical Physics, 18
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • Introduction
  • One-sided reflected Brownian motions and related models
  • Skorokhod construction
  • Packed initial conditions
  • Infinite particle systems
  • Determinantal point processes
  • Definition
  • Fredholm determinants
  • Correlation kernel
  • Strategy for future proofs.-Airy processes.-Elementary Airy processes
  • Crossover Processes
  • Variational identities
  • Gaussian fluctuations of the Airy_stat process
  • Packed and Periodic initial conditions
  • Packed initial conditions
  • Periodic initial conditions
  • Stationary initial conditions
  • Poisson initial conditions
  • Determinantal structure
  • Asymptotic analysis
  • Path-integral style formula
  • Analytic continuation
  • More general initial conditions and their asymptotics
  • Half-Periodic initial conditions
  • Half-Poisson initial conditions
  • Poisson-Periodic initial conditions
  • Attractiveness and a more general class of initial data
  • Asymptotics along space-like paths and slow decorrelations
  • References.